: : : : : : To modify a whole statement, "more important" is the one to choose. "Importantly" means "in an important manner," and "more importantly" should therefore be confined to sentences like "When a reporter was present, the members of the city council walked into the meeting more importantly than usual." At least that's what I was taught. When there's no "more" and we use a single word to modify a whole statement, however, we say "Importantly," not "Important." These two rules don't combine well, logically speaking.

: : : : : The following from The Columbia Guide To Standard American English:

: : : : : "Either the adjectival more/most important or the adverbial more/most importantly may serve as a sentence adverb; both are Standard in this use: More [Most] important [importantly], we now have the right answer."

: : : : : ...and from The American Heritage Dictionary:

: : : : : "Some critics have objected to the use of the phrase more importantly in place of more important when one introduces an assertion, as in More importantly, no one is ready to step into the vacuum left by the retiring senator. But both forms are widely used by reputable writers, and there is no obvious reason for preferring one or the other."

: : : : : I disagree that "importantly" necessarily means "in an important manner". To me, it can also happily and correctly be used to mean "of an important nature".

: : : : : I have no real preference between "more important" and "more importantly" as a sentence qualifier. The adjectival form "more important" may on initial thought seem a little grammatically strange in this usage, but not if one considers it to be an implicit abbreviation of "more important (is the fact that)" or "(a thing which is) more important (is that)".

: : : : Or "(What is) more important." Those critics the Amer. Her. Dict. mentioned must have included my curmudgeonly mentor for editing.

: : : I did note with a smile that the above pasted snippet from the Amer. Her. Dict. includes a sentence starting with the conjunction "But", which in my book is arrant heresy.

: : And it came to pass, he started his sentence with a conjunction.
: : More importantly, he made his meaning clear.
: : Hopefully, everyone understood.

: But seriously, this is one rule I enjoy breaking once in a while. I think it can be very effective.

But seriously, the first word in this sentence is an intensifying adverb and not a conjunction at all. I shan't be burning you at the stake for this.